field (such as electrical potential, temperature, or solute con-A combined analytical-numerical study of the diffusiophoresis centration) that interacts with the surface of each particle. and electrophoresis of a rigid sphere in a uniform applied field A good review of particle motions associated with this mechperpendicular to a plane wall is presented. The range of the interanism, known as ''phoretic motions,'' was given by Anderaction between the solute species and the solid surfaces is assumed son (1).
to be small relative to the particle's radius and to the spacing Perhaps the most familiar example of the various phoretic between the particle and the wall, but the polarization of the difmotions of colloidal particles is electrophoresis, which refuse species in the thin particle-solute interaction layer is allowed.
sults from the interaction between an applied electric field
A slip velocity of fluid and normal fluxes of solute species at the and the electrical double layer surrounding a charged partiouter edge of the thin diffuse layer are used as the boundary conditions for the fluid domain outside the diffuse layer. Through cle. The electrophoretic velocity U 0 of a single nonconductthe use of a collocation method along with these boundary condiing particle suspended in an unbounded fluid is related to tions, a set of conservative equations governing the system is solved the uniformly applied electric field E ฯฑ by the well-known in the quasisteady state situation and the effects of a plane wall Smoluchowski equation (2-4), on diffusiophoresis and electrophoresis are calculated for various cases. For the cases of diffusiophoresis in a nonelectrolyte gradient and of electrophoresis, the particle velocity decreases monotoni-
cally with the decrease of the distance of the particle center from the wall. For the case of diffusiophoresis in an electrolyte gradient, however, the boundary effect is a complicated function of the Here, e/4p is the fluid permittivity, h is the fluid viscosity, properties of the particle and ions, and it no longer varies monotonand z is the zeta potential associated with the particle surface.
ically with the separation distance for some situations. แญง 1996
Another example of phoretic motions is called ''diffusio-Academic Press, Inc.
phoresis'' (4), which is the migration of a solid particle